Plasma generator, plasma control method and method of producing substrate

ABSTRACT

The present invention aims to provide a plasma generator capable of creating a spatially uniform distribution of high-density plasma. This object is achieved by the following construction. Multiple antennas are located on the sidewall of a vacuum chamber, and a RF power source is connected to three or four antennas in parallel via a plate-shaped conductor. The length of the conductor of each antenna is shorter than the quarter wavelength of the induction electromagnetic wave generated within the vacuum chamber. Setting the length of the conductor of the antenna in such a manner prevents the occurrence of a standing wave and thereby maintains the uniformity of the plasma within the vacuum chamber. In addition, the plate-shaped conductor improves the heat-releasing efficiency, which also contributes to the suppression of the impedance.

This application is a continuation application of U.S. patentapplication Ser. No. 10/539,254 filed Jun. 16, 2005, which is a U.S.National Phase application of PCT Application No. PCT/JP2003/016007filed Dec. 12, 2003, which claims priority to Japanese PatentApplications Nos. JP 2003-014718 filed Jan. 23, 2003, JP 2002-363988filed Dec. 16, 2002 and JP 2002-363989 filed Dec. 16, 2002. Thedisclosure of each of these applications is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

The present invention relates to a plasma generator for producing asemiconductor substrate or similar substrates by using plasma to carryout a deposition or etching process on the surface of a base plate to beprocessed. Particularly, the present invention relates to a techniquefor producing a substrate of a large area by uniformly generating aplasma over that area.

BACKGROUND ART

In recent years, the polysilicon TFT-LCD (Thin Film Transistor LiquidCrystal Display) is drawing people's attention because it is capable ofdisplaying images with higher luminance than the TFT-LCD that usesamorphous silicon films. In the production of a polysilicon TFT-LCD, aglass plate is coated with a polysilicon film to create a polysiliconsubstrate. Then, the face of the polysilicon substrate is divided into alarge number of picture elements arrayed in a two-dimensional pattern,and a thin film transistor is formed on each picture element to obtainan LCD substrate. To produce a polysilicon TFT-LCD having a largedisplay area, it is necessary to create a high-quality polysiliconsubstrate that particularly has a high degree of evenness.

Polysilicon substrates are also gathering attention as ahigh-performance solar cell substrate. With the growing demand for andapplication of solar cells, it is necessary for the polysiliconsubstrate to have a larger area. Apart from that, ordinary substratesfor semiconductor devices also need to be produced by a depositionprocess if their area is larger than a single crystal.

The production of substrates used in the aforementioned fields requiresa treatment that uses plasma. This treatment includes the steps ofdepositing a material for the substrate onto a base plate to beprocessed and etching the surface of the same plate. Larger substratesrequire a greated degree of a plasma treatment system. The most seriousproblem for a large-scale system is the unevenness in the plasmatreatment. To avoid this problem, the plasma density should be asuniform as possible over the entire area of the substrate. From theviewpoint of productivity, it is necessary to increase the plasmadensity so as to improve the deposition speed or the etching rate.

Examples of the methods of generating plasma include the ECR (electroncyclotron resonance) plasma, microwave plasma, the inductively coupledplasma and the capacity coupled plasma. In the inductively coupledplasma method, a radiofrequency (RF) voltage is applied to an inductioncoil serving as an antenna to create an induction electromagnetic fieldwithin the plasma generator, whereby plasma is produced. This methodsatisfies one of the aforementioned requirements: the generation ofhigh-density plasma. With regard to the other requirement concerning theimprovement in the uniformity of the plasma density, a variety ofantennas differing in form, position and other factors have beenproposed, taking into account the dependency of the plasma density onthe distance from the antenna. For example, the Japanese UnexaminedPatent Publication No. 2000-58297, which is referred to as the “PatentDocument 1” hereinafter, discloses a technique in which the uniformityof the plasma intensity is improved by introducing an RF wave through aflat coil located on the outside of the ceiling of the plasma-generatingchamber.

To produce a large size substrate using the above-describedconstruction, it is necessary to adequately increase the wall thicknessof the ceiling in the plasma-generating chamber to provide the ceilingwith a sufficient mechanical strength. However, this makes it difficultfor the system of Patent Document 1 to obtain an adequate strength ofelectromagnetic field within the plasma-generating chamber, because theantenna is located outside the plasma-generating chamber and the thickwall attenuates the induction electromagnetic field radiated from theantenna. In summary, the method disclosed in Patent Document 1 iseffective in enhancing the uniformity of the plasma density to a certainextent but cannot adequately increase the plasma density.

To solve this problem, the inventors of the present patent applicationhave proposed that the RF antenna should be located within theplasma-generating chamber, multiple antennas should be used, and eachantenna should have a non-loop shape (i.e. a shape that does notcompletely surround a space), as disclosed in the Japanese UnexaminedPatent Publication No. 2001-35697 (“Patent Document 2”).

This construction enables the electromagnetic field to be fully radiatedwithin the plasma-generating chamber without being attenuated by thewall of the chamber, so that the plasma density is adequately increased.Also, the equally spaced multiple antennas create a highly uniformradiation of electromagnetic field, which improves the uniformity of theplasma intensity. The use of multiple antennas makes the inductance ofeach antenna small enough to prevent an abnormal discharge, which oftentakes place if the antenna is located within the chamber and a highvoltage is applied to the antenna. The non-loop shape of the antennaalso reduces the inductance of the antenna and accordingly contributesto the suppression of the abnormal discharge. With these effectsobtained, it is now possible to carry out a deposition process oretching process on a base plate of a large area. In the followingdescription, the construction using multiple antennas as disclosed inPatent Document 2 is referred to as the “multi-antenna system.”

To process a much larger substrate in the future, it is necessary togenerate a plasma state with a higher degree of uniformity whileensuring an adequate level of plasma density. For that purpose, themulti-antenna system needs to be further examined with respect to theshape, position and other factors of each antenna, the relationshipbetween the antennas, and other parameters that have not beenconsidered. Also, it is possible that the electromagnetic field radiatedfrom the antenna forms a standing wave, which deteriorates theuniformity of the plasma. Furthermore, the multi-antenna system stillallows the plasma density to be lower at the central region of thesubstrate than at the marginal region because the strength of theelectromagnetic field depends on the distance from the RF antenna. Ifthe area of the substrate is small, the difference in plasma densitybetween the central region and the marginal region of the substrate willbe kept within the allowable range. However, the distance cannot beignored for large substrates. Finally, the ion species or the radicalspecies to be created must be also considered because the etching rateor the deposition speed varies depending on the ion species or theradical species.

To address the aforementioned problems, the present invention aims toprovide a plasma generator capable of creating a spatially uniformdistribution of high-density plasma and controlling the type of ionspecies or the radical species to be created.

DISCLOSURE OF THE INVENTION

To solve the above-described problems, the plasma generator according tothe present invention includes:

a) a vacuum chamber;

b) a stage located within the vacuum chamber, on which a base plate isto be placed; and

c) multiple RF antennas arranged substantially parallel to the stagewithin the vacuum chamber.

The plasma generator according to the present invention may preferablyinclude one or more of the following five constructions:

(1) The antenna is a conductor whose length is shorter than the quarterwavelength of the RF wave.

(2) A plate-shaped conductor is connected to the multiple antennas inparallel. The distance between the point at which the power source forsupplying power to the antennas is connected to the plate-shapedconductor and each point at which each antenna is connected to theplate-shaped conductor is shorter than the quarter wavelength of the RFwave.

(3) The aspect ratio of the antenna at a position corresponding to atarget area of the stage is set at a value determined according to theplasma density or plasma electron energy desired for the target area.The “aspect ratio” hereby means the length of the antenna along thedirection perpendicular to the inner wall divided by the length alongthe direction parallel to the inner wall.

(4) The electrodes of the antennas are arranged substantially parallelto the stage, and the adjacent electrodes of one or more pairs ofadjacent antennas have the same polarity.

(5) Impedance elements are connected to the antennas. Preferably, theimpedance elements have variable impedances.

The basic construction of the plasma generator according to the presentinvention is described. The plasma generator according to the presentinvention includes a vacuum chamber having an inner space that serves asthe plasma-generating chamber. The inner space of the vacuum chamber ismaintained at a predetermined degree of vacuum with a vacuum pump.Located in this vacuum chamber is a stage on which the base plate is tobe placed.

Within the vacuum chamber, multiple RF antennas are located. For eachantenna, one electrode is connected to a separately provided powersource and the other is connected to the ground. In an example, theantennas are attached to the sidewall or ceiling wall of the vacuumchamber. These antennas are arranged substantially parallel to thestage.

When an RF power is supplied from the power source to the antennas, eachantenna radiates the induction electromagnetic field, thereby generatingplasma. According to the present invention, the antennas are arrangedroughly parallel to the stage, so that the antennas are at approximatelythe same height from the stage. This arrangement enables the antennas tointensively supply energy into the space, thereby generating plasma withhigh density.

The flat arrangement of the antennas enables the energy to beintensively supplied from the antennas onto a plane area. Therefore, theplasma can have higher densities than in the case of using an antennahaving a three-dimensional shape.

In the case the conductor of an antenna is located within the vacuumchamber, the conductor degrades because the surface of the antenna isexposed to the generated plasma. Therefore, it is preferable to coat thesurface of the antenna with an insulator. This coating also has theeffect of suppressing the electrostatic coupling between the conductorof the antenna and the plasma, thereby preventing an abnormal dischargeor disorder of the plasma. This coating is described in detail in PatentDocument 2.

The plasma generator having the aforementioned construction (1) isdescribed. In this construction, the length of the conductorconstituting each antenna is shorter than the quarter wavelength of theRF power supplied to the antenna. The conductor does not need to have alinear shape. For example, it may be shaped like a plate as long as itslength measured in the direction of the current flow is shorter than thequarter wavelength of the RF wave. This construction prevents theformation of a standing wave on the surface of the conductor, so thatthe uniformity of the plasma within the vacuum chamber is maintained.

The plasma generator having the aforementioned construction (2) isdescribed. In addition to the basic construction described previously,the multiple antennas are now connected to a plate-like conductor inparallel. Through the plate-shaped conductor, the RF power is suppliedfrom the power source to the antennas. To efficiently supply the RFpower to the antennas, it is necessary to reduce the impedance at theconnection between the power source and the antennas. Use of theplate-shaped conductor having an adequate width suppresses the impedanceat the connection. In addition, the plate-shaped conductor improves theheat-releasing efficiency, which also contributes to the suppression ofthe impedance by alleviating the increase in electric resistance thatoccurs when the temperature of the conductor at the connection risesbecause of the power supply.

In the construction (2), a standing wave may be formed between the pointat which the power source supplying the power to the antennas isconnected to the plate-shaped conductor and each point at which eachantenna is connected to the plate-shaped conductor. If this occurs, thestanding wave restricts the magnitude of the RF power supplied to theplate-shaped conductor at the connection point between the power sourceand the plate-shaped conductor. To prevent this situation, the distancebetween the two connection points is made shorter than the quarterwavelength of the RF wave. This prevents the standing wave from takingplace in the plate-shaped conductor, so that the predetermined RF powercan be supplied. It is further preferable that the sum of the length ofthe conductor of the antenna and the distance between the two connectionpoints be smaller than the quarter wavelength of the RF power.

The plasma generator having the aforementioned construction (3) isdescribed. This construction focuses on the aspect ratio of the antenna,which has not been previously considered. The inventors of the presentpatent application have found that the plasma electron energy or theplasma density at the area to which the antenna is directed (i.e. thearea located in the direction perpendicular to the inner wall from thepoint where the antenna is attached) is dependent on the aspect ratio ofan antenna. For example, with a constant RF voltage applied to theantenna, a larger aspect ratio leads to a higher level of plasmaelectron energy at the area to which the antenna is directed. Thepossible reason is as follows: The increased aspect ratio generates astronger induction electric field in the direction of the antenna. Thispotential difference strongly accelerates the plasma electrons, whichare generated around the antenna, along the direction of the antenna.This resultantly increases the plasma electron energy in the arealocated in the direction of the antenna.

The magnitude of the plasma electron energy affects the ion species orradical species created in the aforementioned area due to collisionswith the plasma electrons. A change in the ion species or radicalspecies in turn produces a different etching rate or some otherparameter. Therefore, given a target area in which the etching rate orother parameter is to be controlled, it is possible to control theetching rate or other parameter by changing the aspect ratio of theantenna directed to the target area in order to regulate the plasmaelectron energy and control the ion species or radical species createdin the target area.

The plasma generator having the construction (3) is capable ofcontrolling the electron energy while maintaining the overall electrontemperature in the vacuum chamber at a low level. This enables theelectron energy at the target area to be controlled without raising thepotential of the sheath, which does not contribute to the etching ordeposition process.

Also, the increased aspect ratio further promotes the generation of theplasma by accelerating the plasma electrons and bringing them intocollisions with the remaining molecules of the gas material that havenot become plasma. Thus, the plasma density at the target area isfurther increased.

For a flat antenna having a rectangular, circular or other shape, theaspect ratio is defined as the length of the antenna along the directionperpendicular to the inner wall divided by the length along thedirection parallel to the inner wall. For a three-dimensional antenna, aprojection of the antenna onto a plane parallel to the stage is createdand the aspect ratio is defined as the length of the projection alongthe direction perpendicular to the inner wall divided by the lengthalong the direction parallel to the inner wall.

An example of controlling the plasma electron energy or plasma densityin the plasma generator having the construction (3) is described. Theaspect ratio of the antenna directed to a target area is determinedaccording to the desired value of the plasma electron energy or plasmadensity for the target area. For example, if the plasma density is to beraised over the entire vacuum chamber, the aspect ratios of all theantennas are increased. If the plasma electron energy or plasma densityat a specific area in the vacuum chamber is to be higher, the aspectratio of the antenna directed to the target area is set larger than thatof the other antennas. It is allowable to regulate the aspect ratio ofmore than one antenna. In the case the plasma electron energy or plasmadensity at a specific area in the vacuum chamber is to be decreased, theaspect ratio of the antenna directed to the target area should be lowerthan that of the other antennas. Thus, the plasma electron energy orplasma density can be controlled with a high degree of freedom.

As a typical example of increasing the plasma density at a specific areain the vacuum chamber, the above-described method can be used toincrease the plasma density at the central region of the stage, at whichthe plasma density was lower than at the marginal region in the case ofthe conventional multi-antenna system. Setting the aspect ratio of anantenna directed to the central region larger than that of the otherantennas improves the uniformity in the plasma density over the entireplasma-generating chamber. Using such plasma having an improveduniformity in density, it is possible to uniformly process a substrateover a large area by a deposition or etching process on a base plate.

The method of controlling the plasma density at a specific area in thevacuum chamber may be, for example, applicable to the case where thesubstrate has an uneven portion created for some reason. This problemcan be solved by controlling the plasma density at the uneven portion sothat the deposition speed or etching rate at that portion becomesdifferent from that at the other portion.

The plasma generator having the aforementioned construction (4) isdescribed. With the multiple antennas arranged in the vacuum chamber asin the previous case, the electrodes of the antennas are arrangedsubstantially parallel to the stage, and the adjacent electrodes of theadjacent antennas have the same polarity. This means that both of theadjacent electrodes are connected to either the RF power source or theground.

For example, suppose that an arrangement of the multiple antennas isobtained by placing plural antennas in such a manner that an antennawith one electrode connected to the RF power source and the otherelectrode connected to the earth is translated while maintaining itsconnections. In this case, the adjacent electrodes of the two adjacentantennas resultantly have different polarities. In contrast, if thearrangement of the multiple antennas can be obtained by translating thesame antenna while reversing its connections to the RF power source andthe ground from those of the adjacent antenna, the adjacent electrodesof two adjacent antennas resultantly have the same polarity.

In the case the adjacent electrodes of two adjacent antennas havedifferent polarities, when an RF voltage is applied to the antennas forgenerating an induction electromagnetic field, the same voltage is alsounexpectedly applied between the adjacent electrodes, causing the plasmadensity to be locally high only at that position. As a result, theplasma density becomes lower at the central region of the stage or someother region different from the region between the two adjacentelectrodes. According to the construction (4), in contrast, the adjacentelectrodes of two adjacent antennas have the same polarity. Even when anRF voltage is applied to the antennas, the voltage is not appliedbetween the two adjacent electrodes because they are always at the samepotential. Therefore, the aforementioned local region with higher plasmadensity does not take place between the two adjacent electrodes, and theplasma density is equalized. This construction also allows the adjacentantennas to be placed at narrower intervals and with a larger number ofantennas per unit space without deteriorating the uniformity of theplasma density, so that the overall plasma density can be increased. Itis also possible to control the plasma density distribution byappropriately selecting the combination of the electrodes whose polarityshould be equal.

The plasma generator having the aforementioned construction (5) isdescribed. In this construction, an impedance element for regulating thevoltage or current of the antenna is connected to each antenna. In atypical case, the connection between the antennas and the RF powersource is such that two or more antennas are connected in parallel tothe same RF power source for the purpose of cost reduction or some otherreason. However, it is possible to connect a separate RF power source toeach antenna.

In the case the RF power is supplied from an RF power source to multipleantennas, the RF power supplied to each antenna changes from antenna toantenna depending on the form and the length of the conductor connectingthe RF power source and the antenna, or on the temperature distribution.Particularly, if a plate-shaped conductor is used as the aforementionedconductor, the temperature distribution has a significant influence.Taking this into account, the plasma generator according to the presentconstruction includes the impedance elements whose impedance values canbe regulated so as to reduce the difference in the RF power supplied tothe antennas. This improves the uniformity in the density of the plasmagenerated in the vacuum chamber.

For example, if the aforementioned plate-shaped conductor is used toconnect the multiple antennas to the RF power source in parallel, thetemperature of the plate-shaped conductor is lower at the edge than atthe center due to the heat release from the surface. Therefore, theimpedance value between the RF power source and the antenna connectedclose to the edge of the plate-shaped conductor becomes lower than thatbetween the RF power source and the antenna connected to the centralregion of the plate-shaped conductor. Taking this into account, theimpedance value of the impedance element connected to each antennalocated close to the edge of the plate-shaped conductor is set higher.This setting reduces the difference in the impedance value between eachantenna and the RF power source, so that the RF power supplied to theantennas is leveled.

Even if the plasma density at a specific area in the vacuum space isincreased or decreased for some reason, the density at the area can beapproximated to the value at the other area by regulating the impedancevalue of the impedance element corresponding to the antenna directed tothe area concerned. This setting is also applicable to the case whereeach RF power source has only one antenna connected to it as well as tothe case where multiple antennas are connected to the same RF powersource in parallel.

It is also possible to connect the impedance element only to some of theantennas to regulate the voltage or current of those antennas. In anexample, the maximum power is always supplied to some of the multipleantennas without using any impedance element, whereas the power suppliedto the other antennas is restricted by regulating the impedance valuesof the impedance elements connected to them.

The impedance element connected to the antenna may have a fixed orvariable impedance value. For example, the fixed impedance element canbe used in the case where the impedance values between the RF powersource and the antennas are known in advance and reproducible. Incontrast, the variable impedance element can be used in the case wherethe impedance values between the RF power source and the antennas areunknown, dependent on the temperature or other conditions, or variablewith time, in addition to the previous case. Regulating the impedancevalue of the variable impedance element according to various conditionsand their changes enables the plasma to be uniform in density.

The impedance value of the variable impedance element is preferablyregulated by a feedback process that monitors the state of the plasmawithin the vacuum chamber. This operation can deal with a temporalchange of the plasma density resulting from the temperature change ofthe plate-shaped conductor. For this purpose, it is preferable toprovide the plasma generator according to the present invention with ameasurement unit for measuring a parameter indicative of the state ofthe plasma and a controller for setting the impedance value of eachvariable impedance element on the basis of the parameter. Themeasurement unit may directly determine the plasma density.Alternatively, it may measure the current or voltage for each antenna toindirectly determine the density of the plasma generated.

The measurement unit may be constructed as follows: The current in eachantenna can be easily measured by installing a pick-up coil in proximityto the antenna and measuring the electromotive force induced in thepick-up coil. The voltage across each antenna can be easily measured byinstalling a capacitor in proximity to the antenna and measuring thecurrent flowing into or out of the capacitor. Extending the ends of theconductor constituting the antenna to the outside of the vacuum chamberallows the pick-up coil or the capacitor to be located in proximity tothe ends outside the vacuum chamber. This construction is capable ofmeasuring the current or voltage of the antenna while preventing thepick-up coil or the capacitor from being eroded by the plasma.

The density of the plasma generated is proportional to the powersupplied to the antenna. Therefore, to improve the accuracy of measuringthe plasma density, it is preferable to measure both the current and thevoltage of the antenna, i.e. the power supplied to the antenna, ratherthan to measure only one of them. The value of power can be obtained bymultiplying the signal of the antenna current with the signal of theantenna voltage, both obtained by the methods described previously. Themultiplication can be performed using, for example, a mixer that mixesthe two signals. The signal produced by the mixer contains RFcomponents, and these components should be preferably removed by alow-pass filter. The signal thus obtained is proportional to the powersupplied to the antenna.

In any of the constructions described thus far, it is preferable todivide the multiple antennas into plural groups, each including one ormore antennas, and to supply the RF power to each antenna in parallelwithin each group. Compared to the construction where the power issupplied from a single RF power source to all the antennas, theconstruction having the antenna groups reduces the load on the RF powersource, so that a higher plasma density can be obtained.

The plasma generator having the constructions described thus far iscapable of producing a plasma state having high densities with a higherlevel of uniformity than conventional plasma generators. Use of thisplasma generator enables an efficient production of a substrate having asurface with a higher degree of flatness through the deposition processor etching process.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a vertical sectional view of a plasma generator as the firstembodiment of the present invention.

FIG. 2 is a side view of the plasma generator of the first embodiment.

FIG. 3 is a plan view of the plasma generator of the first embodiment.

FIGS. 4A and 4B are graphs showing the state of the plasma at the centerof the vacuum chamber, which was measured in the plasma generator of thefirst embodiment.

FIGS. 5A and 5B are illustrations showing the plasma densitydistribution within the vacuum chamber, which was measured in the plasmagenerator of the first embodiment.

FIG. 6 is a schematic diagram of an example of a plasma generator havinga phase-adjusting function.

FIG. 7 is a graph showing the change in the plasma density observed whenthe phase difference between the RF power sources was changed.

FIGS. 8A and 8B are plan views of plasma generators that differ fromeach other in the lengths of the conductors of the antennas measuredalong the side wall and in the number of the antennas.

FIG. 9 is a graph showing the plasma potential and the amplitude of thefloating potential, each of which changes with the lengths of theconductors of the antennas measured along the side wall and the numberof the antennas.

FIG. 10 is a plan view of a plasma generator as the second embodiment ofthe present invention.

FIG. 11 is a schematic diagram of three antennas having different aspectratios.

FIG. 12 is a graph showing the plasma density at the center of thevacuum chamber of the plasma generator of the second embodiment and thatof the plasma generator used as a comparative example.

FIG. 13 is a graph showing the plasma electron energy at the center ofthe vacuum chamber of the plasma generator of the second embodiment andthat of a comparative example.

FIG. 14 is a plan view of an example of the plasma generator in whichthe antennas have different aspect ratios.

FIG. 15A is an illustration showing the plasma density distributionobserved in the plasma generator of FIG. 14, and FIG. 15B shows thatobserved in the plasma generator used as a comparative example.

FIG. 16 is a plan view of a plasma generator as the third embodiment ofthe present invention.

FIGS. 17A and 17B are diagrams for explaining the gap between adjacentantennas and the potential difference between them.

FIG. 18 is a graph showing the plasma density at the center of thevacuum chamber of the plasma generator of the third embodiment and thatof the plasma generator used as a comparative example.

FIG. 19 is a graph showing the spatial distribution of the density ofthe plasma generated by the plasma generator of the third embodiment andthat of the plasma generator used as a comparative example.

FIG. 20 is a plan view of a plasma generator as the fourth embodiment ofthe present invention.

FIG. 21 is a diagram showing an example of the impedance element.

FIG. 22 is a vertical section of the plasma generator of the fourthembodiment.

FIG. 23 is a diagram showing an example of the diode bridge circuit.

FIG. 24 is a graph showing the spatial distribution of the density ofthe plasma generated by the plasma generator of the fourth embodiment.

BEST MODE FOR CARRYING OUT THE INVENTION

(First Embodiment)

FIG. 1 is a vertical sectional view of a plasma generator as the firstembodiment of the present invention, FIG. 2 is a side view of the plasmagenerator, and FIG. 3 is a plan view of the plasma generator.

In this plasma generator, the inner space of the vacuum chamber 11serves as the plasma-generating chamber. As shown in FIG. 3, thehorizontal shape of the inner space of the vacuum chamber 11 isrectangular, with the long side measuring 1300 mm and the short side1000 mm. The inner space of the vacuum chamber 11 is maintained at apredetermined degree of vacuum with a vacuum pump (not shown) connectedto the vacuum chamber 11. Located within the vacuum chamber 11 is astage 14 with the long side measuring 94 cm and the short side 76 cm, onwhich a base plate 13 is to be placed. The stage 14 is equipped with anelevating unit 14 a for moving the stage 14 in the vertical direction.At the bottom of the vacuum chamber 11, there is a doorway 12 throughwhich the base plate 13 is inserted into or taken out of the chamber.

Located in the upper space of the vacuum chamber 11 is a gas pipeconsisting of a circulating section making a horizontal turn along inthe inner wall of the vacuum chamber 11 and a connection part that leadsto the outside of the vacuum chamber 11. The gas pipe 15 has a largenumber of perforations arranged on the surface of the circulatingsection to evenly introduce a gas into the vacuum chamber 11.Alternatively, a short pipe penetrating the sidewall and/or the ceilingof the vacuum chamber may be used in place of the gas pipe 15 turning inthe vacuum chamber 11 as in the present embodiment. In that case, it ispreferable to use more than one pipe arranged on the sidewall and/or theceiling in an appropriate pattern to evenly supply the gas into thevacuum chamber 11.

On the four sidewalls of the vacuum chamber 11, there are four pieces ofRF antennas 16 located on each of the horizontally long sidewalls atequal intervals and three pieces of the antennas located on each of theshort sidewalls (see FIG. 3). The antennas 16 are all located at aheight of 180 mm from the stage 14. For each antenna 16, one of the twoelectrodes is connected to the RF power source 18 and the other isconnected to the ground, as described later. In an example, theconnection between one electrode of each antenna and the ground isachieved by connecting the electrode to the sidewall of the vacuumchamber 11 and then connecting the sidewall to the ground. It is alsopossible to connect a fixed or variable blocking condenser to theelectrode in series on the side of the RF power source 18 so that theelectrode is brought into a floating state with respect to the ground.In the present embodiment, the frequency of the power supplied from theRF power source 18 is 13.56 MHz.

The length of the conductor between the two electrodes of the antenna 16is 450 mm, which is shorter than the quarter wavelength (10,000 to15,000 mm) of the RF wave applied to the antenna 16. This designprevents the occurrence of a standing wave, which would deteriorate theuniformity of the plasma.

The portion of the conductor of the antenna 16 that is located withinthe vacuum chamber 11 is coated with an insulator. The RF antenna 16 isU-shaped; it does not form a complete turn. This shape reduces theinductance of the antenna. Detailed descriptions about the antennacoated with the insulator and the antenna having a non-loop shape areavailable in Patent Document 2.

In the present embodiment, the three or four pieces of antennas locatedon each sidewall of the vacuum chamber are connected to the same RFpower source 18 in parallel. As shown in FIG. 2, each antenna 16 isconnected via a plate-shaped conductor 19 to the RF power source 18. Anexample of the plate-shaped conductor 19 is a copper plate extendingalong the outside of the vacuum chamber 11. The RF power source 18 isconnected via an impedance matcher 17 to a point (“power supply point20”) on the copper plate, and one of the electrodes of each antenna 16(indicated by a white spot in FIG. 2) is also connected to the copperplate. The black spots in FIG. 2 denote the grounded electrodes. Thedistance between each electrode of the antenna 16 connected to thecopper plate and the power supply point 20 is shorter than the quarterwavelength of the RF wave applied to the antenna 16. An increase in thewidth of the copper plate will allow the distance to be longer.

The plasma generator of the present embodiment operates as follows: Thestage 14 is lowered with the elevating unit 14 a. A base plate 13 isinserted through the doorway 12 into the vacuum chamber 11 and placed onthe stage 14. Then, the stage 14 is raised to a predetermined position.After the pressure in the vacuum chamber is reduced to a predeterminedlevel, the material gas of the plasma is introduced into the gas pipe 15at a predetermined gas pressure, and a predetermined level of RF poweris supplied from the four RF power sources 18 to the RF antennas 16. Asa result, each of the RF antennas 16 creates an induction electricfield, which generates the plasma.

The following description focuses on the plasma density or plasmaelectron energy generated in the plasma generator of the firstembodiment, referring to the results of experiments.

FIGS. 4A and 4B show the result of a measurement carried out using theplasma generator of the first embodiment, in which the plasma wasproduced from argon (Ar) and the plasma state at the center of thevacuum chamber 11 (a position 160 mm below the inner surface of theceiling wall) was measured using the Langmuir probe method, under thecondition that the flow rate of the argon gas is 50 ccm and the gaspressure is set to 0.66 Pascal and 1.33 Pascal. The data shown in FIG.4A are the plasma potential Vp and the floating potential Vf measuredfor various values of the sum of the RF power supplied to all theantennas 16. The data shown in FIG. 4B are the plasma ion density Ni,the plasma electron density Ne and the plasma electron energy Temeasured for the aforementioned various values of the sum of the RFpower. The plasma potential Vp and the floating potential Vf decreaseswith the increase in the power supplied, while the plasma ion densityNi, the plasma electron density Ne and the plasma electron energy Teincrease with the power. FIGS. 4A and 4B also proves that the plasmagenerator of the first embodiment is capable of generating plasma at alow plasma potential of 20V or lower with a high plasma density of1×10¹¹ or higher. This density is appropriate for various types ofplasma processes.

FIGS. 5A and 5B show the horizontal distribution (or uniformity) of theplasma density measured at a height of 195 mm down from the innersurface of the ceiling wall of the vacuum chamber 11. The measurementresult was evaluated on the basis of the ion saturation current densityobtained by the Langmuir probe method. The ion saturation currentdensity corresponds to the plasma ion density. FIG. 5A shows the resultof a measurement carried out using the plasma generator of the firstembodiment, in which a power of 1000 W was supplied from each of thefour RF power sources 18. In contrast, FIG. 5A shows the result of ameasurement in which each of the RF power sources 18 having fourantennas 16 connected to it generated a power of 1300 W while each ofthe RF power sources 18 having three antennas 16 connected to itgenerated a power of 700 W. The sum of the supplied power is 4000 W inboth cases of FIGS. 5A and 5B. The degree of uniformity in horizontaldistribution of the plasma density in FIG. 5B is higher than in FIG. 5B.Particularly, the plasma density in the area surrounded by the grids ofB, 2, D, 4 is approximately uniform. This result shows that the plasmadensity distribution can be controlled by regulating the power suppliedfrom each RF power source to the antennas.

FIG. 6 shows the construction of a plasma generator having the functionof adjusting the phase of the RF power of each RF power source. Thisplasma generator is equipped with waveform detectors (or phasedetectors) 21, each located at the output of the impedance matcher 19provided for each of the RF power sources 18 a-18 d. At requiredintervals, the waveform detector 21 acquires the waveform of the RFpower supplied to the antennas 16 and sends the waveform signal to aphase adjuster 22, which in turn detects the phase difference betweenthe RF power sources 18. Based on the detection result, phase adjuster22 sends a phase control signal to each of the RF power source 18 sothat the phase difference is adjusted to a predetermined value. Each ofthe RF power sources 18 adjusts the phase of the RF power it generates.

FIG. 7 shows the result of a measurement carried out using the plasmagenerator of FIG. 6, in which the plasma density was measured forvarious values of the phase difference between the RF power sources. InFIG. 7, the coordinate axis indicates the plasma electron density Ne ata measurement point located close to the center of the vacuum chamber.The abscissa axis indicates the phase differences between the RF powersources 18 a and 18 b, 18 b and 18 c, and 18 c and 18 d. The resultshows that the plasma density increased with the phase difference. Thisis probably because the phase difference between two antennasaccelerated the electrons between the antennas and resultantly causedthe increase in plasma density. The strength of accelerating theelectrons should vary depending on the shape of the antenna, thedistance between the antennas, the gas pressure, the size of the vacuumchamber 11 and other factors. Taking this into account, the phasedifference is appropriately regulated so that the plasma density reachesthe highest level.

FIGS. 8A and 8B show examples of the plasma generator of the firstembodiment, in which the length α of the conductor of the antenna alongthe direction of the sidewall is set longer while the number of theantennas is reduced. In FIG. 8A, the vacuum chamber is provided with twopieces of antennas 23 a located on the inside of each of the longersidewalls and two pieces of antennas 24 a located on the inside of eachof the shorter sidewalls, where the length a of the antenna 23 a is 1.56times as long as that of the antenna in FIG. 3 and the length a of theantenna 24 a is 1.27 times. In FIG. 8B, the vacuum chamber has oneantenna 23 b on each of the insides of the longer sidewall and oneantenna 24 b on the inside of each of the shorter sidewalls, where thelength a of the antenna 23 b is 2.67 times as long as that of theantenna in FIG. 3 and the length a of the antenna 24 b is 2.20 times.These constructions are accompanied by a larger inductance of theantenna due to the use of a longer conductor and an increased RF powersupplied to each antenna increases because of the smaller number of theantennas.

FIG. 9 shows the result of a measurement using the plasma generators ofFIGS. 3, 8A and 8B, in which the amplitudes of the plasma potential andthe floating potential were measured. The use of longer conductors forthe antennas and a smaller number of the antennas for each power sourceleads to larger amplitudes of the plasma potential and the floatingpotential. This is probably due to an increase in the impedance of theantennas and due to an increase in the potential of the antennas due tothe smaller number of antennas for each power source. An increase in theamplitudes of the plasma potential and the floating potential may causea heavier damage on the ions during the plasma process. However, it isstill useful in the case of producing plasma of hydrogen, helium orother gases that have high ionization energies.

(Second Embodiment)

The plasma generator of the second embodiment is featured by the aspectratio of the antennas, as described below.

FIG. 10 is a plan view of the second embodiment. The construction ofthis plasma generator is identical to that of the first embodimentexcept for the antennas 26 having a different aspect ratio. Therefore,FIG. 10 uses the same numerals used in FIG. 3 for the components thatare also present in the first embodiment. The number of the RF powersources and the number of the antennas connected to each RF power sourceare also the same as those in the first embodiment. In the plasmagenerator shown in FIG. 10, the aspect ratio of every antenna 26 is setto 2 (length: width=2:1), as shown in FIG. 11A, whereas the aspect ratioof the antenna 16 in the first embodiment is 1 (length: width=1:1), asshown in FIG. 11B. The area S enclosed by the conductor of the antenna26 in the second embodiment is the same as that of the antenna 16 in thefirst embodiment.

The following description focuses on the plasma density or plasmaelectron energy generated in the plasma generator of the secondembodiment, referring to the results of experiments. To examine theinfluence of the aspect ratio, the experiments were carried out usingthree types of the plasma generators having the aspect ratio of all theantennas set to 2 (the present embodiment using the antenna shown inFIG. 11A), 1 (the first embodiment using the antenna shown in FIG. 11B)and 0.5 (using the antenna shown in FIG. 11C), respectively. The lengthof each edge of the RF antenna having the aspect ratio of 1 was 15 cm.In this experiment, argon gas was supplied into the vacuum chamber up toa gas pressure of 1.33 Pascal, and an RF power with a frequency of 13.56MHz was supplied to the antennas to generate argon plasma. The plasmadensity was measured by the Langmuir probe method.

FIG. 12 shows the result of a measurement in which the plasma densitywas measured at the height equal to that of the RF antennas and abovethe center of the stage. The coordinate axis indicates the plasmadensity with a logarithmic scale and the abscissa axis indicates themagnitude of the RF power supplied from each RF power source. Under thecondition that the RF power is constant, the plasma generator of thepresent embodiment using the RF antennas having the aspect ratio of 2provides a higher plasma density than the other plasma generator usingthe RF antennas having the aspect ratio of 1 or 0.5.

FIG. 13 shows the result of a measurement in which the energydistribution of the plasma electrons was measured above the center ofthe stage, using the same three plasma generators as used in themeasurement shown in FIG. 12. The magnitude of the RF power suppliedfrom each RF power source was set to 2000 W. The setting of the otherparameters was the same as in the measurement shown in FIG. 12. Thecoordinate axis is the logarithmic scale. Within the energy range of 10to 18 eV, the plasma generator having the aspect ratio of 2 produces agreater number of plasma electrons than the other plasma generatorshaving the other aspect ratios. These high-energy electrons result fromthe acceleration of electrons by the potential difference that takesplace in the RF antenna. The traveling direction of these electrons isaffected by the aspect ratio. In the U-shaped RF antenna used in thepresent embodiment, the high-energy electrons are created along thelongitudinal direction of the RF antenna. Therefore, a greater number ofhigh-energy electrons are observed in the case the aspect ratio is 2than in the case the aspect ratio is 1 or 0.5.

The result shown in FIG. 13 also suggests that the energy of theelectrons in the plasma can be controlled by changing the aspect ratioof the RF antennas. This also enables the control of the ion species,radical species or other factors that are important for the plasmaprocess.

In the next example, the aspect ratio of each antenna is differentlydetermined, as shown in the plan view of FIG. 14. In the plasmagenerator shown in FIG. 14, two of the four pieces of the RF antennas oneach of the longer sidewalls of the vacuum chamber 11 are centrallylocated and have the aspect ratio of 2 (for example, the RF antenna 26a). Similarly, one of the three pieces of the RF antennas on each of theshorter sidewalls is centrally located and has the aspect ratio of 2.The other RF antennas located next to each of the four corners of thevacuum chamber 11 have the aspect ratio of 1 (for example, the antenna26 b).

The construction embodies the idea that the aspect ratio of the antennasdirected to the center of the stage should be set larger than that ofthe other antennas in order to increase the plasma density at the targetarea, i.e. the center of the stage.

FIG. 15A shows the result of a measurement carried out using the plasmagenerator show in FIG. 14, in which the spatial distribution of theplasma density was measured at the height equal to that of the RFantennas. For comparison, FIG. 15B shows the result of the samemeasurement carried out using a plasma generator in which the entire RFantennas have an aspect ratio of 1. Each RF power source supplied an RFpower of 1000 W. Other conditions relating to the generation of theplasma were the same as in the second embodiment. FIGS. 15A and 15B showthat, in the plasma generator shown in FIG. 14, the plasma density atthe central region is higher than that in the comparative example,whereas the increase in the plasma density at the marginal region issuppressed. As a result, the level of uniformity in the plasma densityis higher than that in the comparative example.

(Third Embodiment)

The plasma generator of the third embodiment is featured by thepolarities of the adjacent electrodes of two adjacent antennas, asdescribed below.

FIG. 16 is a plan view of the third embodiment. The components that arepresent in the first embodiment are denoted by the same numeral as usedin FIG. 3. The number of RF power sources and the number of antennasconnected each RF power source are the same as in the first embodiment.The construction of the present plasma generator is identical to that inthe first embodiment except for the RF antennas 16 whose electrodes havedifferent polarities. More specifically, among each antenna groupincluding three or four pieces of RF antennas located on the samesidewall, two adjacent electrodes of two adjacent RF antennas have thesame polarity. Taking the antenna group 31 a as an example, both of thetwo adjacent electrodes of the two adjacent RF antennas 16 a and 16 bare connected to the impedance matcher 17 and the RF power source 18,and the two adjacent electrodes of the two adjacent RF antennas 16 b and16 c are connected to the ground.

If, as shown in FIG. 17B, the adjacent terminals of adjacent RF antennashave different polarities, a potential difference takes place across thegap 32 between the adjacent electrodes of the adjacent antennas.Therefore, the plasma density at the gap 32 becomes higher than at theother positions. Accordingly, the plasma density at the other positionsdecreases. Conversely, in the plasma generator of the third embodiment,the adjacent terminals of adjacent RF antennas have the same polarity,so that the potential difference across the gap 32 between the adjacentelectrodes is always zero. This construction prevents the increase inthe plasma density that would take place across the gap 32 if apotential difference was present between the adjacent terminals. Thedecrease in the plasma density at the other region is also prevented.

The following description shows the result of a measurement in which thedensity of the plasma generated in the plasma generator of the thirdembodiment was measured. In this experiment, argon gas was supplied intothe vacuum chamber up to a gas pressure of 1.33 Pascal, and an RF powerwith a frequency of 13.56 MHz was supplied to the antennas to generateargon plasma. Other conditions will be explained later when eachmeasurement is described. The plasma density was measured by theLangmuir probe method.

FIG. 18 shows the result of a measurement carried out using the plasmagenerator of the third embodiment, in which the plasma density wasmeasured at the height equal to that of the RF antennas and above thecenter of the stage. FIG. 18 also shows the result of a measurementcarried out using a plasma generator in which the adjacent electrodeswere made to have different polarities for the purpose of comparison.The coordinate axis indicates the plasma density with a logarithmicscale and the abscissa axis indicates the magnitude of the RF powersupplied from each RF power source. For any value of the RF power, theplasma generator of the present embodiment provides higher plasmadensities than the plasma generator of the comparative example.Particularly, when the value of the RF power is in the range from 1200 Wto 2500 W, the density of the plasma generated in the present embodimentis approximately twice as high as that in the comparative example.

FIG. 19 shows the result of a measurement of the spatial distribution ofthe plasma density. The measurement conditions are as follows: The RFpower is supplied only to the antenna group 31 b shown in FIG. 16. Themagnitude of the RF power supplied from the RF power source is 1500 W.The abscissa axis in FIG. 19 indicates the points at which the plasmadensity was measured. These points lie on a horizontal line parallel toand at a distance of 13 cm from the sidewall on which the antenna group31 b is located. FIG. 19 shows that, in the plasma generator of thecomparative example, the plasma density at the ends is lower than thatmeasured at the center; the spatial distribution of the plasma densityis uneven. In contrast to the comparative example, the unevenness in thespatial distribution of the plasma is reduced in the plasma generator ofthe present embodiment. Thus, the uniformity in the spatial distributionof the plasma density is improved.

(Fourth Embodiment)

The plasma generator of the second embodiment is featured by animpedance element connected to the antenna, as described below.

FIG. 20 is a plan view of the fourth embodiment. The components that arepresent in the first embodiment are denoted by the same numeral as usedin FIG. 3. The number of RF power sources and the number of antennasconnected each RF power source are the same as in the first embodiment.In addition to the construction of the first embodiment, the presentplasma generator includes an impedance element 41 inserted between oneof the electrodes of each RF antennas 16 and the impedance matcher 17.For example, the variable inductance coil 42 shown in FIG. 21 can beused. The inductance value of the variable inductance coil 42 may bemanually regulated. However, for the feedback control described later,it is preferable to use a driver 43 to automatically regulate theinductance value. In this embodiment, the impedance element 41 isconnected to the electrode of the antenna 16 on the side of the RF powersource 20, which may be otherwise connected to the grounded electrode.

In the fourth embodiment, a pick-up coil 44 and a capacitor 45 areinstalled as shown in the vertical sectional view of FIG. 23. A portionof the RF antenna 16 is projected to the outside of the vacuum chamber11. Therefore, the pick-up coil 44 and the capacitor 45 may bepreferably located close to the projected portion so that they may notbe eroded by the plasma. The pick-up coil 44, which is used to measurethe current, can be located either on the grounded side or on thepower-supplied side of the antenna 16. A bridge circuit 46, as shown inFIG. 22, is connected to each of the pick-up coil 44 and the capacitor45 to convert the alternating-current (AC) signal generated by thepick-up coil 44 and the capacitor 45 into a direct-current (DC) signal.Alternatively, a wave detector that detects an AC signal and generates aDC signal may be used in place of the bridge circuit. In addition, thereis a controller 47 that receives the aforementioned signals andgenerates a signal for regulating the impedance value of the impedanceelement 41 (FIG. 20).

In the present embodiment, if an uneven distribution of the plasmadensity occurs due to a temperature distribution of the copper plate 19or for some other reason, the plasma generator equalizes the plasmadensity by regulating the impedance value of each impedance element 41to appropriately control the power supplied to each RF antenna 16. Fixedimpedance elements may be used if the plasma distribution observed isreproducible and the desirable impedance value can be identified throughexperiments or in some other way. In the case the distribution of theplasma density varies depending on the gas used, the power supplied orother factors and the distribution is reproducible under the sameconditions, it is possible to use variable impedance elements and setthe impedance values according to the conditions. If the change orreproducibility of the plasma density distribution depending on theconditions is not clear, the impedance value of the variable impedanceelement should be regulated by a feedback control based on the plasmadensity distribution.

The aforementioned feedback control is carried out as follows: Thecontroller 47 receives a current signal from the pick-up coil 44 and/ora voltage signal from the capacitor 45 located at each antenna. For anyone of the antennas, if one of the signals, or a signal indicating thepower obtained by multiplying the two signals together, has exceeded apredetermined value, or if the plasma density around the antennaconcerned has exceeded the a predetermined value, the controller 47sends a signal for increasing the impedance to the driver 43corresponding to the impedance element 41 connected to theaforementioned antenna. Conversely, if the current signal or othersignal observed at an antenna is below a predetermined value, thecontroller 47 sends a signal for decreasing the impedance to the driver43. Upon receiving a signal from the controller 47, the driver 43 setsthe impedance of the corresponding impedance element to a predeterminedvalue. Thus, the plasma density around the impedance element ismaintained within a predetermined range.

The following description relates to an experiment in which the densitydistribution of the plasma generated by the plasma generator of thisembodiment was measured. In this experiment, the RF power was suppliedonly to the three antennas A, B and C surrounded by the broken line inFIG. 20. The plasma density was measured along a line at a distance of13 cm from the sidewall of the vacuum chamber on which theaforementioned three antennas were located, using the Langmuir probemethod. The plasma generated in the experiment was argon plasma. Argongas was supplied to a gas pressure of 1.33 Pascal, and RF power of 2000W and 13.56 MHz was supplied from a single RF power source to the threeantennas A, B and C.

The plasma density was measured under three conditions in which theratio of the magnitudes of the currents flowing through the antennas A,B and C was 1:1.2:1, 2:1:2 and 3:1:3, respectively. These conditionswere created by regulating the impedance value of each impedance elementaccording to the signal from the pick-up coil 44. FIG. 24 shows themeasurement result. In the case the current ratio is 1:1.2:1, thecurrents flowing through the three antennas are almost equal, and theplasma density is higher at the center than at the marginal region. Inthe case the current ratio is 2:1:2, the currents flowing through the RFantennas located at both ends are increased, and the plasma densitydecreases at the center and increases at the marginal region. Thus, theuniformity of the plasma density is improved.

In the case the current ratio is 3:1:3, in which the currents flowingthrough the RF antennas at both ends are further increased, the plasmadensity is low at the center, in contrast to the case of the currentratio 1:1.2:1.

The current ratio that provides the optimal distribution of the plasmadensity depends on the type and the pressure of the plasma gas, thepower supplied from the RF power source and other factors. Therefore,the impedance value of each impedance element should be appropriatelyregulated so that the current ratio takes the optimal valuescorresponding to the conditions.

In the embodiments described thus far, the horizontal shape of thevacuum chamber is rectangular, which may be alternatively shapedcircular or otherwise. Also, some or all of the antennas may be locatedon the ceiling of the vacuum chamber, as opposed to the foregoingembodiments in which the antennas are located on the sidewalls of thevacuum chamber.

The invention claimed is:
 1. A plasma generator comprising: a) a vacuumchamber; b) a stage located within the vacuum chamber on which a baseplate is to be placed; and c) multiple U-shaped RF antennas arrangedsubstantially parallel to the stage within the vacuum chamber, whereinan aspect ratio of a U-shaped RF antenna directed to a center of thestage is larger than that of other U-shaped RF antennas while areasenclosed by conductors of the multiple U-shaped RF antennas areconstant, the aspect ratio defined as a length of the RF antenna along adirection perpendicular to an inner wall divided by a length of the RFantenna along a direction parallel to the inner wall.
 2. The plasmagenerator according to claim 1, wherein the RF antennas are attached onone or both of a sidewall and a ceiling wall of the vacuum chamber. 3.The plasma generator according to claim 1, wherein a surface of the RFantennas is coated with an insulator.
 4. The plasma generator accordingto claim 1, wherein the shape of the RF antennas within the vacuumchamber is flat.
 5. The plasma generator according to claim 1, whereineach of the multiple RF antennas are divided into groups each includingone or more RF antennas, and a RF power is supplied to each RF antennain parallel within each group.
 6. A method of producing a substrate,wherein plasma of a material is generated by a plasma generatoraccording to claim 1 and the material is deposited.
 7. A method ofproducing a substrate, wherein an etching process is carried out usingplasma generated by a plasma generator according to claim
 1. 8. A plasmacontrol method comprising: providing a plasma generator having multipleU-shaped RF antennas located within a vacuum chamber, said antennasbeing arranged on one or both of a sidewall and a ceiling wall of thevacuum chamber and substantially parallel to a stage on which a baseplate is to be placed, wherein an aspect ratio of a U-shaped RF antennadirected to a center of the stage is set to a larger value than that ofother U-shaped RF antennas while areas enclosed by conductors of themultiple U-shaped RF antennas are constant, the aspect ratio defined asa length of the RF antenna along a direction perpendicular to an innerwall divided by a length of the RF antenna along a direction parallel tothe inner wall.